arXiv subjects

Craig D. Roberts

Publications and source records attributed to Craig D. Roberts.

At least 91 records · Page 5Linked to original sources

arXiv2020

Contact interaction analysis of pion GTMDs

A contact interaction is used to calculate an array of pion twist-two, -three and -four generalised transverse light-front momentum dependent parton distribution functions (GTMDs). Despite the interaction's simplicity, many of the results are physically relevant, amongst them a statement that GTMD size and shape are largely prescribed by the scale of emergent hadronic mass. Moreover, proceeding from GTMDs to generalised parton distributions (GPDs), it is found that the pion's mass distribution form factor is harder than its electromagnetic form factor, which is harder than the gravitational pressure distribution form factor; the pressure in the neighbourhood of the pion's core is commensurate with that at the centre of a neutron star; the shear pressure is maximal when confinement forces become dominant within the pion; and the spatial distribution of transversely polarised quarks within the pion is asymmetric. Regarding transverse momentum dependent distribution functions (TMDs), their magnitude and domain of support decrease with increasing twist. The simplest Wigner distribution associated with the pion's twist-two dressed-quark GTMD is sharply peaked on the kinematic domain associated with valence-quark dominance; has a domain of negative support; and broadens as the transverse position variable increases in magnitude.

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arXiv2020

Empirical Consequences of Emergent Mass

The Lagrangian that defines quantum chromodynamics (QCD), the strong interaction piece of the Standard Model, appears very simple. Nevertheless, it is responsible for an astonishing array of high-level phenomena with enormous apparent complexity, e.g., the existence, number and structure of atomic nuclei. The source of all these things can be traced to emergent mass, which might itself be QCD's self-stabilising mechanism. A background to this perspective is provided, presenting, inter alia, a discussion of the gluon mass and QCD's process-independent effective charge and highlighting an array of observable expressions of emergent mass, ranging from its manifestations in pion parton distributions to those in nucleon electromagnetic form factors.

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arXiv2020

Selected Science Opportunities for the EicC

An electron ion collider has been proposed in China (EicC). It is anticipated that the facility would provide polarised electrons, protons and ion beams, in collisions with large centre-of-mass energy. This discussion highlights its potential to address issues that are central to understanding the emergence of mass within the Standard Model, using examples that range from the exploration of light-meson structure, through measurements of near-threshold heavy-quarkonia production, and on to studies of the spectrum of exotic hadrons.

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arXiv2020

Impressions of the Continuum Bound State Problem in QCD

Modern and anticipated facilities will deliver data that promises to reveal the innermost workings of quantum chromodynamics (QCD). In order to fulfill that promise, phenomenology and theory must reach a new level, limiting and overcoming model-dependence, so that clean lines can be drawn that connect the data with QCD itself. Progress in that direction, made using continuum methods for the hadron bound-state problem, is sketched herein.

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arXiv2020

Reflections upon the Emergence of Hadronic Mass

With discovery of the Higgs boson, science has located the source for $\lesssim 2$% of the mass of visible matter. The focus of attention can now shift to the search for the origin of the remaining $\gtrsim 98$%. The instruments at work here must be capable of simultaneously generating the 1 GeV mass-scale associated with the nucleon and ensuring that this mass-scale is completely hidden in the chiral-limit pion. This hunt for an understanding of the emergence of hadronic mass (EHM) has actually been underway for many years. What is changing are the impacts of QCD-related theory, through the elucidation of clear signals for EHM in hadron observables, and the ability of modern and planned experimental facilities to access these observables. These developments are exemplified in a discussion of the evolving understanding of pion and kaon parton distributions.

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arXiv2020

Nucleon elastic form factors at accessible large spacelike momenta

A Poincaré-covariant quark+diquark Faddeev equation is used to compute nucleon elastic form factors on $0\leq Q^2\leq 18 \,m_N^2$ ($m_N$ is the nucleon mass) and elucidate their role as probes of emergent hadronic mass in the Standard Model. The calculations expose features of the form factors that can be tested in new generation experiments at existing facilities, e.g. a zero in $G_E^p/G_M^p$; a maximum in $G_E^n/G_M^n$; and a zero in the proton's $d$-quark Dirac form factor, $F_1^d$. Additionally, examination of the associated light-front-transverse number and anomalous magnetisation densities reveals, inter alia: a marked excess of valence $u$-quarks in the neighbourhood of the proton's centre of transverse momentum; and that the valence $d$-quark is markedly more active magnetically than either of the valence $u$-quarks. The calculations and analysis also reveal other aspects of nucleon structure that could be tested with a high-luminosity accelerator capable of delivering higher beam energies than are currently available.

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arXiv2020

Semileptonic decays of $D_{(s)}$ mesons

A symmetry-preserving continuum approach to meson bound-states in quantum field theory, employed elsewhere to describe numerous $π$- and $K$-meson electroweak processes, is used to analyse leptonic and semileptonic decays of $D_{(s)}$ mesons. Each semileptonic transition is conventionally characterised by the value of the dominant form factor at $t=0$ and the following results are obtained herein: $f_+^{D_s\to K}(0) = 0.673(40)$; $f_+^{D\to π}(0)=0.618(31)$; and $f_+^{D\to K}(0)=0.756(36)$. Working with the computed $t$-dependence of these form factors and standard averaged values for $|V_{cd}|$, $|V_{cs}|$, one arrives at the following predictions for the associated branching fractions: ${\cal B}_{D_s^+\to K^0 e^+ ν_e} = 3.31(33)\times 10^{-3}$; ${\cal B}_{D^0\to π^- e^+ ν_e} = 2.73(22)\times 10^{-3}$; and ${\cal B}_{D^0\to K^- e^+ ν_e} = 3.83(28)$%. Alternatively, using the calculated $t$-dependence, agreement with contemporary empirical results for these branching fractions requires $|V_{cd}|=0.221(9)$, $|V_{us}|=0.953(34)$. With all $D_{(s)}$ transition form factors in hand, the nature of SU$(3)$-flavour symmetry-breaking in this array of processes can be analysed; and just as in the $π$-$K$ sector, the magnitude of such effects is found to be determined by the scales associated with emergent mass generation in the Standard Model, not those originating with the Higgs mechanism.

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arXiv2019

Effective charge from lattice QCD

Using lattice configurations for quantum chromodynamics (QCD) generated with three domain-wall fermions at a physical pion mass, we obtain a parameter-free prediction of QCD's renormalisation-group-invariant process-independent effective charge, $\hatα(k^2)$. Owing to the dynamical breaking of scale invariance, evident in the emergence of a gluon mass-scale, this coupling saturates at infrared momenta: $\hatα(0)/π=0.97(4)$. Amongst other things: $\hatα(k^2)$ is almost identical to the process-dependent (PD) effective charge defined via the Bjorken sum rule; and also that PD charge which, employed in the one-loop evolution equations, delivers agreement between pion parton distribution functions computed at the hadronic scale and experiment. The diversity of unifying roles played by $\hatα(k^2)$ suggests that it is a strong candidate for that object which represents the interaction strength in QCD at any given momentum scale; and its properties support a conclusion that QCD is a mathematically well-defined quantum field theory in four dimensions.

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arXiv2019

Drawing insights from pion parton distributions

A symmetry-preserving continuum approach to the two valence-body bound-state problem is used to calculate the valence, glue and sea distributions within the pion; unifying them with, inter alia, electromagnetic pion elastic and transition form factors. The analysis reveals the following momentum fractions at the scale $ζ_2:=2\,$GeV: $\langle x_{\rm valence} \rangle = 0.48(3)$, $\langle x_{\rm glue} \rangle = 0.41(2)$, $\langle x_{\rm sea} \rangle = 0.11(2)$; and despite hardening induced by the emergent phenomenon of dynamical chiral symmetry breaking, the valence-quark distribution function, ${q}^π(x)$, exhibits the $x\simeq 1$ behaviour predicted by quantum chromodynamics (QCD). After evolution to $ζ=5.2\,$GeV, the prediction for ${q}^π(x)$ matches that obtained using lattice-regularised QCD. This confluence should both stimulate improved analyses of existing data and aid in planning efforts to obtain new data on the pion distribution functions.

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arXiv2019

Unveiling the structure of pseudoscalar mesons

A valuable approach to the analysis of hadron physics observables is provided by QCD's equations-of-motion; namely, the Dyson-Schwinger equations. Drawing from a diverse collection of predictions, we revisit: $γγ^* \to$ neutral pseudoscalar transition form factors, their corresponding valence-quark distribution amplitudes and a recent result on the pion distribution functions.

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arXiv2019

Two photon transition form factors of neutral pseudoscalar mesons

Starting from the axial vector Ward-Green-Takahashi identity, and the necessity of preserving this identity when attempting to calculate the properties describing pseudoscalar mesons, we describe a Bethe-Salpeter kernel which takes into account the non-Abelian anomaly and therefore is suitable to describe the flavor mixing states $η,η^\prime$. We then report results for the two photon transition form factors of $η,η^\prime$, and compare them with existing experimental data.

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arXiv2019

Form factors for the Nucleon-to-Roper electromagnetic transition at large-$Q^2$

We report on a recent calculation of all Roper-related electromagnetic transtions form factors, covering the range of energies that next-to-come planned experiments are expected to map. Direct reliable calculations were performed, within a Poincaré covariant approach of the three-body bound-state problem, up to $Q^2/m^2_N$=6; approximated then by applying the Schlessinger point method and the results eventually extended up to $Q^2/m^2_N\simeq$12 via analytic continuation.

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arXiv2019

Process-independent effective coupling and the pion structure function

We sketch the calculation of the pion structure functions within the DSE framework, following two alternative albeit consistent approaches, and discuss then their QCD evolution, the running driven by an effective charge, from a hadronic scale up to any larger one accessible to experiment.

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arXiv2019

Insights into the Origin of Mass

Atomic nuclei are the core of everything we can see. At the first level of approximation, their atomic weights are simply the sum of the masses of all the nucleons they contain. Each nucleon has a mass $m_N \approx 1\,$GeV, i.e. approximately 2000-times the electron mass. The Higgs boson produces the latter, but what produces the nucleon mass? This is the crux: the vast bulk of the mass of a nucleon is lodged with the energy needed to hold quarks together inside it; and that is supposed to be explained by quantum chromodynamics (QCD), the strong-interaction piece within the Standard Model. This contribution canvasses the potential for a coherent effort in QCD phenomenology and theory, coupled with experiments at existing and planned facilities, to reveal the origin and distribution of mass by focusing on the properties of the strong-interaction Nambu-Goldstone modes. Key experiments are approved at JLab 12; planned with COMPASS++/AMBER at CERN; and could deliver far-reaching insights by exploiting the unique capabilities foreseen at an electron ion collider.

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arXiv2019

Resonance Electroproduction and the Origin of Mass

One of the greatest challenges within the Standard Model is to discover the source of visible mass. Indeed, this is the focus of a "Millennium Problem", posed by the Clay Mathematics Institute. The answer is hidden within quantum chromodynamics (QCD); and it is probable that revealing the origin of mass will also explain the nature of confinement. In connection with these issues, this perspective describes insights that have recently been drawn using contemporary methods for solving the continuum bound-state problem in relativistic quantum field theory and how they have been informed and enabled by modern experiments on nucleon-resonance electroproduction.

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arXiv2019

Pion and Kaon Structure at the Electron-Ion Collider

Understanding the origin and dynamics of hadron structure and in turn that of atomic nuclei is a central goal of nuclear physics. This challenge entails the questions of how does the roughly 1 GeV mass-scale that characterizes atomic nuclei appear; why does it have the observed value; and, enigmatically, why are the composite Nambu-Goldstone (NG) bosons in quantum chromodynamics (QCD) abnormally light in comparison? In this perspective, we provide an analysis of the mass budget of the pion and proton in QCD; discuss the special role of the kaon, which lies near the boundary between dominance of strong and Higgs mass-generation mechanisms; and explain the need for a coherent effort in QCD phenomenology and continuum calculations, in exa-scale computing as provided by lattice QCD, and in experiments to make progress in understanding the origins of hadron masses and the distribution of that mass within them. We compare the unique capabilities foreseen at the electron-ion collider (EIC) with those at the hadron-electron ring accelerator (HERA), the only previous electron-proton collider; and describe five key experimental measurements, enabled by the EIC and aimed at delivering fundamental insights that will generate concrete answers to the questions of how mass and structure arise in the pion and kaon, the Standard Model's NG modes, whose surprisingly low mass is critical to the evolution of our Universe.

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arXiv2019

Spectrum and structure of octet and decuplet baryons and their positive-parity excitations

A continuum approach to the three valence-quark bound-state problem in quantum field theory, employing parametrisations of the necessary kernel elements, is used to compute the spectrum and Poincaré-covariant wave functions for all flavour-$SU(3)$ octet and decuplet baryons and their first positive-parity excitations. Such analyses predict the existence of nonpointlike, dynamical quark-quark (diquark) correlations within all baryons; and a uniformly sound description of the systems studied is obtained by retaining flavour-antitriplet--scalar and flavour-sextet--pseudovector diquarks. Thus constituted, the rest-frame wave function of every system studied is primarily $S$-wave in character; and the first positive-parity excitation of each octet or decuplet baryon exhibits the characteristics of a radial excitation. Importantly, every ground-state octet and decuplet baryon possesses a radial excitation. Hence, the analysis predicts the existence of positive-parity excitations of the $Ξ$, $Ξ^\ast$, $Ω$ baryons, with masses, respectively (in GeV): 1.84(08), 1.89(04), 2.05(02). These states have not yet been empirically identified. This body of analysis suggests that the expression of emergent mass generation is the same in all $u$, $d$, $s$ baryons and, notably, that dynamical quark-quark correlations play an essential role in the structure of each one. It also provides the basis for developing an array of predictions that can be tested in new generation experiments.

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arXiv2019

Transition form factors: $γ^\ast + p \to Δ(1232)$, $Δ(1600)$

Electroproduction form factors describing the $γ^\ast p \to Δ^+(1232), Δ^+(1600)$ transitions are computed using a fully-dynamical diquark-quark approximation to the Poincaré-covariant three-body bound-state problem in relativistic quantum field theory. In this approach, the $Δ(1600)$ is an analogue of the Roper resonance in the nucleon sector, appearing as the simplest radial excitation of the $Δ(1232)$. Precise measurements of the $γ^\ast p \to Δ^+(1232)$ transition already exist on $0 \leq Q^2 \lesssim 8\,$GeV$^2$ and the calculated results compare favourably with the data outside the meson-cloud domain. The predictions for the $γ^\ast p \to Δ^+(1600)$ magnetic dipole and electric quadrupole transition form factors are consistent with the empirical values at the real photon point, and extend to $Q^2 \approx 6 m_p^2$, enabling a meaningful direct comparison with experiment once analysis of existing data is completed. In both cases, the electric quadrupole form factor is particularly sensitive to deformation of the $Δ$-baryons. Interestingly, whilst the $γ^\ast p \to Δ^+(1232)$ transition form factors are larger in magnitude than those for $γ^\ast p \to Δ^+(1600)$ in some neighbourhood of the real photon point, this ordering is reversed on $Q^2 \gtrsim 2 m_p^2$, suggesting that the $γ^\ast p \to Δ^+(1600)$ transition is more localised in configuration space.

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